Challenge Level

In this problem you have to place four by four magic squares on the faces of a cube so that along each edge of the cube the numbers match.

Challenge Level

Number problems at primary level that may require resilience.

Challenge Level

Find out what a Deca Tree is and then work out how many leaves there will be after the woodcutter has cut off a trunk, a branch, a twig and a leaf.

Challenge Level

On the planet Vuv there are two sorts of creatures. The Zios have 3 legs and the Zepts have 7 legs. The great planetary explorer Nico counted 52 legs. How many Zios and how many Zepts were there?

Challenge Level

Cassandra, David and Lachlan are brothers and sisters. They range in age between 1 year and 14 years. Can you figure out their exact ages from the clues?

Challenge Level

Place the digits 1 to 9 into the circles so that each side of the triangle adds to the same total.

Challenge Level

There are 4 jugs which hold 9 litres, 7 litres, 4 litres and 2 litres. Find a way to pour 9 litres of drink from one jug to another until you are left with exactly 3 litres in three of the jugs.

Challenge Level

The clockmaker's wife cut up his birthday cake to look like a clock face. Can you work out who received each piece?

Challenge Level

Skippy and Anna are locked in a room in a large castle. The key to that room, and all the other rooms, is a number. The numbers are locked away in a problem. Can you help them to get out?

Challenge Level

Add the sum of the squares of four numbers between 10 and 20 to the sum of the squares of three numbers less than 6 to make the square of another, larger, number.

Challenge Level

Number problems at primary level that require careful consideration.

Challenge Level

Annie cut this numbered cake into 3 pieces with 3 cuts so that the numbers on each piece added to the same total. Where were the cuts and what fraction of the whole cake was each piece?

Challenge Level

Can you put plus signs in so this is true? 1 2 3 4 5 6 7 8 9 = 99 How many ways can you do it?

Challenge Level

Can you substitute numbers for the letters in these sums?

Challenge Level

This magic square has operations written in it, to make it into a maze. Start wherever you like, go through every cell and go out a total of 15!

Challenge Level

On the table there is a pile of oranges and lemons that weighs exactly one kilogram. Using the information, can you work out how many lemons there are?

Challenge Level

Rocco ran in a 200 m race for his class. Use the information to find out how many runners there were in the race and what Rocco's finishing position was.

Challenge Level

Try adding together the dates of all the days in one week. Now multiply the first date by 7 and add 21. Can you explain what happens?

Challenge Level

48 is called an abundant number because it is less than the sum of its factors (without itself). Can you find some more abundant numbers?

Challenge Level

There are three buckets each of which holds a maximum of 5 litres. Use the clues to work out how much liquid there is in each bucket.

Challenge Level

Fill in the missing numbers so that adding each pair of corner numbers gives you the number between them (in the box).

Challenge Level

On a calculator, make 15 by using only the 2 key and any of the four operations keys. How many ways can you find to do it?

Challenge Level

There are 44 people coming to a dinner party. There are 15 square tables that seat 4 people. Find a way to seat the 44 people using all 15 tables, with no empty places.

Challenge Level

Put the numbers 1, 2, 3, 4, 5, 6 into the squares so that the numbers on each circle add up to the same amount. Can you find the rule for giving another set of six numbers?

Challenge Level

Can you score 100 by throwing rings on this board? Is there more than way to do it?

Challenge Level

There is a clock-face where the numbers have become all mixed up. Can you find out where all the numbers have got to from these ten statements?

Challenge Level

There are 78 prisoners in a square cell block of twelve cells. The clever prison warder arranged them so there were 25 along each wall of the prison block. How did he do it?

Challenge Level

I was looking at the number plate of a car parked outside. Using my special code S208VBJ adds to 65. Can you crack my code and use it to find out what both of these number plates add up to?

Challenge Level

Use your logical reasoning to work out how many cows and how many sheep there are in each field.

Challenge Level

Using the statements, can you work out how many of each type of rabbit there are in these pens?

Challenge Level

This task, written for the National Young Mathematicians' Award 2016, invites you to explore the different combinations of scores that you might get on these dart boards.

Challenge Level

A group of children are using measuring cylinders but they lose the labels. Can you help relabel them?

Challenge Level

If the numbers 5, 7 and 4 go into this function machine, what numbers will come out?

Challenge Level

Start by putting one million (1 000 000) into the display of your calculator. Can you reduce this to 7 using just the 7 key and add, subtract, multiply, divide and equals as many times as you like?

Challenge Level

Zumf makes spectacles for the residents of the planet Zargon, who have either 3 eyes or 4 eyes. How many lenses will Zumf need to make all the different orders for 9 families?

Challenge Level

What do you notice about the date 03.06.09? Or 08.01.09? This challenge invites you to investigate some interesting dates yourself.

Challenge Level

Can you draw a continuous line through 16 numbers on this grid so that the total of the numbers you pass through is as high as possible?

Challenge Level

Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.

Challenge Level

What do the digits in the number fifteen add up to? How many other numbers have digits with the same total but no zeros?

Challenge Level

Here are the prices for 1st and 2nd class mail within the UK. You have an unlimited number of each of these stamps. Which stamps would you need to post a parcel weighing 825g?

Challenge Level

The Scot, John Napier, invented these strips about 400 years ago to help calculate multiplication and division. Can you work out how to use Napier's bones to find the answer to these multiplications?

Challenge Level

Mrs Morgan, the class's teacher, pinned numbers onto the backs of three children. Use the information to find out what the three numbers were.

Challenge Level

This problem is based on the story of the Pied Piper of Hamelin. Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!

Challenge Level

Where can you draw a line on a clock face so that the numbers on both sides have the same total?

Challenge Level

There were chews for 2p, mini eggs for 3p, Chocko bars for 5p and lollypops for 7p in the sweet shop. What could each of the children buy with their money?

Challenge Level

Winifred Wytsh bought a box each of jelly babies, milk jelly bears, yellow jelly bees and jelly belly beans. In how many different ways could she make a jolly jelly feast with 32 legs?

Challenge Level

You have 5 darts and your target score is 44. How many different ways could you score 44?